In advanced physics, the concept of symmetry plays a crucial role in understanding fundamental interactions and the laws governing the universe. Can you explain how Noether's theorem connects symmetries and conservation laws in theoretical physics? Specifically, how does the presence of continuous symmetries in a physical system lead to conserved quantities, and what are some practical examples of this connection in classical mechanics, quantum mechanics, and field theory? Additionally, how does gauge symmetry extend this concept in the context of the Standard Model of particle physics, contributing to our understanding of fundamental forces?